How are the scarlet letter "A" and the child Pearl alike?
In 'The Scarlet Letter.'

The scarlet letter "A" and her daughter Pearl testify to what Hester has done and are symbols of shame; but at the same time they both distinguish her as being apart from and even above the rest of the community. (Her position on the scaffold does the same thing.)

Hester bears the "A" on her bosom as an emblem of her identity (incidentally, much as the Jews would wear the star of David during the Nazi regime), and its presence somehow emboldens her to assume her life since she has nothing to hide. Unlike Dimmesdale, the father of the child, Hester does not cower in the shadows or pretend to be someone she is not; by wearing the "A" ("A"for Adultery) without flinching, Hester gains a certain dignity and self-respect by doing so.

Sprite-like Pearl, skipping among the light and shadow of the forest, is both Hester's burden and solace. Pearl cannot offer her mother the same kind of companionship as that of an adult, but her very presence breaks her solitude just the same. Her name is symbolic, too, in that the consequence of Hester's stigma for committing adultery is the gift of a beautiful child, untainted by the reproach which falls upon the mother. Pearl is indeed her pearl; and if before the eyes of the community the child is first considered a malediction, to Hester her daughter is a bittersweet consolation.

It is paradoxical that Hester Prynn devotes her life in service to a community which in essence has rejected her;although not a Christ figure per se, Hester nevertheless embodies the ideals of both sacrifice and atonement. Even the vividly red "A" she bears loses its original association; does it still mean 'adultery' as originally intended, or 'acquitted' or 'absolved,' or even 'angel?' (A far cry Hester is indeed from the personality of Dimmesdale, who succumbs under the weight of hypocrisy and pride. By such a flagrant contrast of characterization, Hawthorne deftly raises the important question of the real meaning of 'purity' within the New England 'Puritan' congregation and on a broader scope as well).

To sum up, the letter "A" and Pearl are alike in that they originally are negative in connotation by exposing Hester as an adulteress, but in the end they are emblems of her virtue instead.